Ok, thank you, I didn't think of the lossy compression.
Anyway I've found a discussion on another forum where someone says that you can send fax over a GSM network if your carrier allows it (the carrier implements the fax protocol). Chances are that you have to pay for this extra service.

I don't know if it is allowed to post link to other forums, anyway I found the thread with the help of google searching for "send fax gsm".

Later in the morning I could ask my carrier if it allows it and if I have to pay extra money.

L-